Final answer:
To calculate the diameter of the hose, use the formula for volume flow rate and solve for the area of the hose. Then, use the formula for the area of a circle to calculate the diameter.
Step-by-step explanation:
To calculate the diameter of the hose, we can use the formula for volume flow rate:
Q = A * v
Where:
Q is the volume flow rate
A is the cross-sectional area of the hose
v is the velocity of water
We are given the volume flow rate, 600 L, and the velocity, 4.0 m/s. First, we convert the volume flow rate from liters to cubic meters:
Q = 0.6 m3
Next, we can rearrange the formula to solve for the area of the hose:
A = Q / v
Substituting the values:
A = 0.6 m3 / 4.0 m/s = 0.15 m2
Finally, we can calculate the diameter of the hose using the formula for the area of a circle:
A = π * (d/2)2
Where:
d is the diameter of the hose
Rearranging the formula:
d = 2 * √(A / π)
Substituting the value of A:
d = 2 * √(0.15 m2 / π)
= 2 * √(0.0477)
≈ 2 * 0.218
= 0.436 m
= 43.6 cm
Therefore, the diameter of the hose is approximately 43.6 cm.